The precise locations of the DNase I cutting sites in the nucleosome core have been determined by analysis of the DNA products of a DNase I digestion of 32P end-labelled mucleosome cores on a high resolution gel electrophoresis system. This system is capable of resolving fragments of mixed sequence DNA differing by one base into the region of 160 bases in length. The DNase I cutting sites in the core are found to be spaced at multiples of about 10.4 (i.e. clearly different from 10.0) bases along the DNA, but show significant variations about this value. In addition to the location of the sites, the stagger between individual sites on opposite strands has been determined and is found to be inconsistent with at least one proposed mechanism for nuclease cleavage of chromatin DNA. Finally, a calculated distribution of fragment lengths in a DNase I digest of nuclei has been determined from the data obtained from the nucleosome core and found to be in reasonable agreement with the observed distribution. The periodicity of 10.4 is discussed with respect to the number of base pairs per turn of chromatin DNA and the number of superhelical turns of DNA per nucleosome.